I'm working in industry and have an application requiring some expert knowledge on statistics/probability. I have a probability distribution function (PDF) for a Gaussian random variable. I know the standard deviation of the PDF. I also know total number of experiments conducted, where one experiment is one value of the random variable, x.

For example, the standard deviation in my application is 1 ps RMS (e.g. 1 ps = 1E-12 seconds). The number of measured values for my random variable is 600E+9 (e.g. 600E+9 individual values of x; I don't have the individual values, but I know 600E+9 of them were measured).

From this information, I need to predict the largest peak-to-peak deviation (e.g. the width of the PDF, from the end of one tail to the end of the other tail) that may be observed (as a function of a given confidence level, or confidence interval, not sure what's the right terminology here; I believe this level/interval is needed to define the goal, correct me if not).

Can anyone help me understand the equations involved? I know Gaussian PDF for random variable x is

PDF(x) = (1/sigma*sqrt(2*pi))*e^(x*x/(2*sigma^2))

Not sure how to quantify the largest peak-peak deviation expected based on number o acquired samples N and sigma. Thanks in advance. -Tim